CN101936780A - A wavefront sensor with two cone mirrors - Google Patents

Abstract

The invention relates to a wavefront sensor with two conical mirrors, which consists of four lenses, two conical mirrors, a beam splitter and two CCD image detectors; the incident distorted wavefront is firstly divided into two paths by a beam splitter, each path of light passes through a 4f beam-shrinking system consisting of two-sided cone mirrors and two lenses, ridge edges of the two-sided cone mirrors are mutually orthogonally arranged, and the ridge edges are respectively superposed with the focuses of the first lens or the third lens, one of the two-sided cone mirrors splits the front edge of the incident distorted wave in the horizontal direction, the other two-sided cone mirror splits the front edge of the incident distorted wave in the vertical direction, and then pupil conjugate images of the two-sided cone mirrors are imaged to respective CCD image detectors after passing through the second lens or the fourth lens; the CCD image detector is connected with a computer, the computer is used for reading pupil images, the light intensity distribution difference of the two pupil images in the horizontal direction or the vertical direction is compared to obtain measurement signals in the two directions, and then the wavefront phase is reconstructed by utilizing a wavefront restoration algorithm.

Description

A wavefront sensor with two cone mirrors

technical field

The invention relates to a wavefront sensor, in particular to a wavefront sensor with two conical mirrors, which belongs to key devices in the technical fields of adaptive optics, wavefront detection and the like.

Background technique

The wavefront sensor is an important device for measuring wavefront distortion in an adaptive system. According to the connection between the measurement signal and the wavefront, it can be divided into two categories: one is to obtain the wavefront by measuring the slope of the wavefront (ie, the first derivative of the wavefront) Phase, the more typical Hartmann wavefront sensor, shearing interferometer, etc.; the other is to measure the wavefront curvature (ie, the second derivative of the wavefront) to obtain the wavefront phase, mainly curvature wavefront sensor.

The most commonly used Hartmann wavefront sensor uses a microlens array to segment the entrance pupil, and calculates the wavefront slope by measuring the difference between the centroid coordinates of the image spot on the focal plane of the lens array and the reference wavefront centroid coordinates. Another pupil-splitting wavefront sensor uses N (N>1) pyramids to split the incident wavefront to measure wavefront distortion (US Patent US4399356 "Optical wavefront sensing system" issued in 1983).

These two types of wavefront sensors are wavefront sensors that divide the wavefront, and their spatial sampling rate is determined by the number of sub-apertures. Each sub-aperture needs several CCD pixels to detect the center of the spot, and increasing the number of sub-apertures will affect the photoelectric imaging element. The number of pixels puts forward higher requirements, and the utilization rate of light energy is low.

The Australian patent AU2003267457A1 "Pyramid sensor for determining the wave aberration of the human eye" authorized in 2002 uses a pyramid-shaped refracting mirror to divide the converging incident light into 4 beams at the focal plane, and then uses a relay lens to image the image to the CCD image detector. The measured signal is obtained by comparing the light intensity difference of the pupil image in the same direction, and then the wavefront to be measured is restored by using the linear reconstruction matrix. This sensor is called a pyramidal wavefront sensor (PWFS). Compared with the previous two sub-wavefront wavefront sensors, each pixel of the CCD is equivalent to a sub-aperture, which has the advantages of high sampling rate, easy change, and high light energy utilization (A&A, 350, L23-L26, 1999, Opt. Commun, 268, 189-195, 2006).

The core device of PWFS is a pyramid-shaped refracting prism, referred to as quadrangular pyramid. Its function is to split the incident wave in the spectrum, so there are strict requirements on its surface roughness and edge platform width (SPIE, Vol. 4007, 423-430, 2000). Although the technology of processing quadrangular pyramids has been continuously improved, it is still difficult to produce qualified quadrangular pyramids at present, and it is easy to produce a wider platform at the tip of the edge of the roof, thus affecting the wavefront detection (Microelectronic Engineering67-68, 566-573, 2003 ; PhD Thesis, Joana Büchler costa. 2005). In addition, when using the non-modulated PWFS to measure the wavefront difference, the reconstruction matrix used to restore the wavefront by the mode method has no analytical solution and needs to be measured on site (Appl. Opt, 47, 79-87, 2008).

Contents of the invention

The purpose of the present invention is to use the wavefront sensor with two conical mirrors to overcome the low spatial sampling rate and low light energy utilization rate of the traditional Hartmann wavefront sensor, the difficulty in making the quadrangular pyramidal wavefront sensor and the need for linear reconstruction matrix in the actual optical path. Disadvantages of taking measurements.

In order to achieve the stated purpose, the technical solution of the wavefront sensor with two axicons provided by the present invention is: with two axicons, a beam splitter BS, four lenses and two CCD image detectors, the incident distortion The wavefront is divided into two beams of light by the beam splitter BS, and each light passes through a 4f beam reduction system composed of a two-sided axicon and two lenses. The two roof edges of the two two-sided axicons are placed orthogonally to each other, and Their roof edges coincide with the focal points of the first lens or the third lens respectively. One of the two axicons splits the incident distorted wavefront in the horizontal direction, and the other two axicons split the incident distorted wavefront in the vertical direction, and then passes through the first After the second lens or the fourth lens, the pupil conjugate images are imaged to the respective CCD image detectors; the two lenses of the 4f beam reduction system share a focal plane, and the focal lengths of the two lenses are not equal; the CCD image detectors Connect with the computer, use the computer to read the pupil image, and compare the light intensity distribution difference of the two pupil images in the horizontal direction or vertical direction to obtain the measurement signals in the two directions, and then use the wavefront restoration algorithm to reconstruct the wavefront phase .

Compared with the prior art, the present invention has the following advantages:

(1) Compared with the Hartmann wavefront sensor, the wavefront sensor with two conical mirrors of the present invention has the advantages of high sampling rate (same CCD target surface) and high utilization rate of light energy.

(2) In the wavefront sensor of the double-sided axicon of the present invention, the used two-sided axicon is easy to process, and the edge is only formed by two planes, so it is not easy to produce a platform.

(3) The wavefront sensor of the two-sided cone mirror of the present invention, compared with the quadrangular pyramidal wavefront sensor, when adopting the model method to restore the wavefront, the reconstruction matrix can be calculated without on-site measurement by the analytical formula, and has a larger ratio than the quadrangular pyramidal wavefront sensor Higher wavefront restoration accuracy.

Description of drawings

Fig. 1 is the schematic diagram of the wavefront sensor of two conical mirrors of the present invention;

Figure 2a is a schematic diagram of the light intensity of the pupil image obtained by the first CCD image detector after splitting light along the horizontal direction;

Fig. 2b is the pupil image distribution diagram on the first CCD image detector after the coma aberration is split along the horizontal direction;

Figure 3a is a schematic diagram of the light intensity of the pupil image obtained by the second CCD image detector after splitting light along the horizontal direction;

Fig. 3b is the pupil image distribution diagram on the second CCD image detector after the coma aberration is split along the horizontal direction;

Fig. 4a to Fig. 4c are the simulation results of coma aberration wavefront restoration by the wavefront sensor of the two conical mirrors of the present invention using the mode method.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

As shown in Figure 1, the principle diagram of the wavefront sensor of the two-sided axicon of the present invention, the present invention is made of two two-sided axicons, a beam splitter BS, four lenses and two CCD image detectors. The incident distorted wavefront is divided into two beams of light by the beam splitter BS, and each light passes through a 4f narrowing system composed of a two-sided cone mirror and two lenses L ₁ , L ₂ (or two lenses L ₃ , L ₄ ). The two roof edges of the two two-sided axicons are placed orthogonally to each other, and their roof edges coincide with the focal points of the first lens _L1 or the third lens _L3 respectively, and one of the two-sided axicons will incident the distortion wavefront The light is split in the horizontal direction, and then through the second lens L ₂ , another two-sided cone mirror splits the light in the vertical direction of the incident distorted wavefront, and then after passing through the fourth lens L ₄ , the pupil conjugate image is imaged to the respective CCD image detectors . Among them, the two lenses of the 4f beam reduction system share a focal plane, and the focal lengths of the two lenses are not equal; the two CCD image detectors are connected to the computer respectively, and the pupil image is read by the computer, and the horizontal or vertical direction is compared The light intensity distribution difference of the two pupil images can obtain the measurement signals in two directions, and then the wavefront phase can be reconstructed by using the wavefront restoration algorithm.

The beam splitter BS has an arbitrary beam splitting ratio.

Described two two-sided axicons comprise the first two-sided axicon 1 and the second two-sided axicon 2, and the first two-sided axicon 1 has the first roof edge 11 and the second two-sided axicon 2 has the first two-sided axicon 2. Two roof edges 21, the first roof edge 11 and the second roof edge 21 are placed orthogonally to each other, respectively placed on the focal planes of the first lens L ₁ and the third lens L ₃ , and the first roof edge The edge 11 and the second roof edge 21 are at the focal point of the first lens L ₁ and the third lens L ₃ .

决定光瞳像大小，其中，D为入射波前孔径。Among the four lenses, the focal lengths of the first lens L ₁ and the third lens L ₃ are respectively f ₁ , the focal lengths of the second lens L ₂ and the fourth lens L ₄ are respectively f ₂ ,

Determine the pupil image size, where D is the incident wavefront aperture.

M为相邻的光瞳像中心距离与光瞳像的比值，f₁为第一透镜L₁和第三透镜L₃的焦距，n为材料的折射率。Described two-sided axicon is the refraction type two-sided axicon that traditional optics processing technology makes; The base angle of two-sided axicon

M is the ratio of the center distance of adjacent pupil images to the pupil image, f ₁ is the focal length of the first lens L ₁ and the third lens L ₃ , n is the refractive index of the material.

The ratio of the center distance of the adjacent pupil images to the pupil images is M>2.

中间的棱宽小于

所述两面锥镜的顶角接近180°，λ为波长。The bottom surface and the roof surface of the two cone mirrors are plated with an anti-reflection film, and the surface shape is

The middle rib width is less than

The apex angle of the two conical mirrors is close to 180°, and λ is the wavelength.

The pixel sizes of the two CCD image detectors are equal, and the shortest length of the target surface of each CCD image detector is greater than

两个解析式给出，其中，P(x)和P(y)分别表示过探测点(x，y)垂直于坐标轴y和x的直线与光瞳函数P边界的交点，λ为波长，(x′，y′)表示坐标系(x，y)中任意点的坐标，所以无需现场测量。When the model method is used for wavefront restoration, the distorted wavefront to be measured can be described as Among them, Z _m (x, y) is the Zernike polynomial of order m, a _m is the corresponding coefficient, N represents the Zernike order taken, and (x, y) is the coordinate of the distortion wavefront to be measured. The response matrix used consists of N column vectors, and the mth column vector is given by

Two analytical formulas are given, wherein, P(x) and P(y) respectively represent the intersection point of the line perpendicular to the coordinate axes y and x through the detection point (x, y) and the boundary of the pupil function P, λ is the wavelength, (x', y') represents the coordinates of any point in the coordinate system (x, y), so no on-site measurement is required.

Let the light field at the entrance pupil of the wavefront sensor with two conical mirrors be:

${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; i</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

where u ₀ and φ(x, y) represent the amplitude and phase of the incident light field respectively, x and y represent the coordinates of the distortion to be measured, i represents the imaginary part unit, P is the pupil function, λ is the wavelength, and the incident light field is The beam splitter BS is divided into two paths, and the ratio of its transmittance to reflectivity is equal to a/b. After the two paths of light pass through the two conical mirrors and the 4f system respectively, the pupil image formed on the target surface of the CCD image detector, among them I ₁ and I ₂ are the light intensity of the pupil image obtained by the first CCD image detector after splitting light in the horizontal direction of the distortion wavefront to be measured, and its distribution is shown in Fig. 2a; Fig. 2b is the coma aberration (the seventh-order Zernike mode, Z ₇ ) Pupil image distribution diagram on the first CCD image detector after light splitting along the horizontal direction; _I3 and _I4 are the light formed after the vertical direction splitting of the distortion wavefront to be measured obtained by the second CCD image detector The distribution of the light intensity of the pupil image is shown in Fig. 3a; Fig. 3b is the distribution diagram of the pupil image on the second CCD image detector after the coma aberration (7th order Zernike mode, Z ₇ ) is split along the horizontal direction. By comparing the light intensity difference between two pupil images in the same direction, the measurement signals S _x and S _y can be obtained. The relationship between the measurement signal and the distorted wavefront is:

In the formulas (2) and (3), the upper and lower limits of integration P(x) and P(y) represent the intersection points of the line perpendicular to the coordinate axes y and x and the boundary of the pupil function P through the detection point (x, y), respectively, ( x', y') represent the coordinates of any point in the coordinate system (x, y). f ₁ and f ₂ respectively denote the focal lengths of two lenses in the 4f system, the two lenses being the first lens L ₁ and the third lens L ₃ , the second lens L ₂ and the fourth lens L ₄ .

Z_m(x，y)为第m阶的Zernike多项式，a_m为相应的系数，N表示所取的Zernike阶数。当

较小时，公式(2)和(3)中的正弦函数可用其泰勒展开式中的第一项来近似表示，于是上面两式可以写成：Use the Zernike mode to represent the measured distortion wavefront aberration:

Z _m (x, y) is the Zernike polynomial of order m, a _m is the corresponding coefficient, and N represents the Zernike order taken. when

When small, the sine function in formulas (2) and (3) can be approximated by the first term in its Taylor expansion, so the above two formulas can be written as:

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\underset{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}{\overset{\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\frac{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\underset{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}{\overset{\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\frac{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; xm</span>}}<span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}{\overset{\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\frac{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; ym</span>}}<span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}{\overset{\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\frac{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

较大时，公式(2)和(3)到公式(4)和(5)的近似过程将会产生较大的误差，因而测量结果只能体现待测畸变波前的方向。这时可以使用变形镜对入射光场进行负反馈校正，使校正后残余相位误差逐渐减小，直至达到需要的校正精度为止，从而通过这种闭环操作可以得到待测畸变波前。S _x and S _y are the linear superposition of signals G _xm and G _ym of each order when the coefficients of the first N order Zernike terms are small. When the aberration to be measured

When it is larger, the approximation process from formulas (2) and (3) to formulas (4) and (5) will produce larger errors, so the measurement results can only reflect the direction of the distortion wavefront to be measured. At this time, the deformable mirror can be used to perform negative feedback correction on the incident light field, so that the residual phase error after correction is gradually reduced until the required correction accuracy is achieved, so that the measured distortion wavefront can be obtained through this closed-loop operation.

When using the model method for wavefront restoration, the analytical solutions of G _xm and G _ym can be solved in advance, and then numerically discretized according to the spatial sampling rate of the actual optical system, thereby establishing a linear response matrix G. At this time, formulas (4) and ( The matrix form of 5) can be expressed as S=GA, A is the Zernike coefficient vector, and the generalized inverse G ⁺ of this response matrix is further obtained by using the singular value decomposition method (SVD). M represents the spatial sampling rate of the distorted wavefront to be measured, N represents the order of the Zernike mode taken when the mode is restored, and the Zernike coefficients of each order of the wavefront to be measured are calculated by the following formula:

A＝G ⁺ S. (8)

in, $A=\left[\begin{array}{c}{a}_1\\ a_2\\ \&CenterDot;\&Center\; Dot;\&Center\; Dot;\\ a_N\end{array}\right];$ $G=\left[\begin{array}{cccc}{G}_{x1}\left(1\right)& G_{x2}\left(1\right)& \&Center\; Dot;\&Center\; Dot;\&Center\; Dot;& G_{\mathrm{xN}}\left(1\right)\\ G_{\mathrm{the\; y}1}\left(1\right)& G_{\mathrm{the\; y}2}\left(1\right)& \&Center\; Dot;\&CenterDot;\&CenterDot;& G_n\left(1\right)\\ G_{x1}\left(2\right)& G_{x2}\left(2\right)& \&CenterDot;\&Center\; Dot;\&Center\; Dot;& G_{\mathrm{xN}}\left(2\right)\\ G_{\mathrm{the\; y}1}\left(2\right)& G_{\mathrm{the\; y}2}\left(2\right)& \&CenterDot;\&CenterDot;\&CenterDot;& G_n\left(2\right)\\ \&CenterDot;\&CenterDot;\&Center\; Dot;& \&Center\; Dot;\&Center\; Dot;\&Center\; Dot;& \&Center\; Dot;\&Center\; Dot;\&CenterDot;& \&Center\; Dot;\&Center\; Dot;\&Center\; Dot;\\ G_{x1}\left(m\right)& G_{x2}\left(m\right)& \&Center\; Dot;\&Center\; Dot;\&Center\; Dot;& G_{\mathrm{xN}}\left(m\right)\\ G_{\mathrm{the\; y}1}\left(m\right)& G_{\mathrm{the\; y}2}\left(m\right)& \&Center\; Dot;\&Center\; Dot;\&Center\; Dot;& G_n\left(m\right)\end{array}\right];$ $S=\left[\begin{array}{c}{S}_x\left(1\right)\\ S_{\mathrm{the\; y}}\left(1\right)\\ S_x\left(2\right)\\ S_{\mathrm{the\; y}}\left(2\right)\\ \&Center\; Dot;\&Center\; Dot;\&CenterDot;\\ S_x\left(m\right)\\ S_{\mathrm{the\; y}}\left(m\right)\end{array}\right]$

When the wavefront is measured by a two-sided conical wavefront sensor, the items of the response matrix G can be directly calculated by the analytical formula (6) and (7), while the corresponding expression of the square pyramid contains the cross term between the signals, and the analytical formula cannot be used get.

Fig. 4a to Fig. 4c are the simulation results of the wavefront restoration of the coma (the 7th order Zernike mode, Z ₇ ) by the wavefront sensor of the two conical mirrors of the present invention using the mode method, wherein Fig. 4a is the original wavefront, and Fig. 4b is the restoration wavefront, Figure 4c is the residual wavefront.

The above is only a specific implementation mode in the present invention, but the scope of protection of the present invention is not limited thereto. Anyone familiar with the technology can understand the conceivable transformation or replacement within the technical scope disclosed in the present invention. All should be covered within the scope of protection of the claims of the present invention.

Claims (9)

1. A wavefront sensor having a two-sided axicon, characterized by: the two-sided cone mirror is provided with two-sided cone mirrors, a beam splitter BS, four lenses and two CCD image detectors, an incident distortion wavefront is divided into two beams of light by the beam splitter BS, each path of light passes through a 4f beam-shrinking system consisting of the two-sided cone mirrors and the two lenses, two ridge edges of the two-sided cone mirrors are orthogonally arranged, the ridge edges of the two ridge mirrors are respectively superposed with the focus of the first lens or the third lens, one of the two-sided cone mirrors divides the horizontal direction of the incident distortion wavefront, the other two-sided cone mirror divides the vertical direction of the incident distortion wavefront, and then pupil conjugate images of the two-sided cone mirrors are imaged to the respective CCD image detectors after passing through the second lens or the fourth lens; wherein two lenses of the 4f beam-shrinking system share one focal plane, and the focal lengths of the two lenses are different; the CCD image detector is connected with a computer, the computer is used for reading pupil images, the light intensity distribution difference of the two pupil images in the horizontal direction or the vertical direction is compared to obtain measurement signals in the two directions, and then the wavefront phase is reconstructed by utilizing a wavefront restoration algorithm.

2. The wavefront sensor of claim 1 with a two-sided cone mirror, wherein: the beam splitter has an arbitrary splitting ratio.

3. The wavefront sensor of claim 1 with a two-sided cone mirror, wherein: the two-sided cone mirrors comprise a first two-sided cone mirror and a second two-sided cone mirror, the first two-sided cone mirror is provided with a first ridge edge, the second two-sided cone mirror is provided with a second ridge edge, the first ridge edge and the second ridge edge are orthogonally arranged, focal planes of the first lens and the third lens are respectively placed, and the first ridge edge and the second ridge edge are just opposite to the focuses of the first lens and the third lens.

4. The wavefront sensor of claim 1 with a two-sided cone mirror, wherein: the focal lengths of the first lens and the third lens in the four lenses are respectively f₁The focal lengths of the second lens and the fourth lens are respectively f₂，

The pupil image size is determined, where D is the incident wavefront aperture.

5. The wavefront sensor of claim 1 with a two-sided cone mirror, wherein: the two-sided cone mirror is a refraction type two-sided cone mirror manufactured by a traditional optical device processing technology; of two-sided conical mirrorsBottom corner

M is the ratio of the central distance of the adjacent pupil images to the pupil image, f₁Is the focal length of the first lens and the third lens, and n is the refractive index of the material.

6. The wavefront sensor of claim 5 with a two-sided cone mirror, wherein: the ratio of the central distance of the adjacent pupil images to the pupil image is M & gt 2.

7. The wavefront sensor of claim 1 with a two-sided cone mirror, wherein: the bottom surface and the ridge surface of the two-sided cone mirror are plated with antireflection films, and the surface shape

The width of the middle edge is less thanThe vertex angle of the two-sided cone mirror is close to 180 degrees, and lambda is the wavelength.

8. The wavefront sensor of claim 1 with a two-sided cone mirror, wherein: the pixels of the two CCD image detectors are equal in size, and the shortest length of the target surface of each CCD image detector is larger than that of the target surface of the other CCD image detector

9. The wavefront sensor of claim 1 with a two-sided cone mirror, wherein: when the wave front is restored by adopting the mode method, the distorted wave front to be measured can be described as

Wherein Z_m(x, y) is a Zernike polynomial of order m, a_mThe order of the Zernike is taken as N and the coordinate of the distorted wavefront to be measured is (x, y); the response matrix used is composed of N column vectors, the m column vector is composed of

Two analytical expressions are given, where P (x) and P (y) denote the intersection of the straight lines perpendicular to the coordinate axes y and x and the boundary of the pupil function P, respectively, of the over-detection point (x, y), λ is the wavelength, and (x ', y') denotes the coordinates of any point in the coordinate system (x, y), so no in-situ measurement is required.

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